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Adaptive optimal control using value iteration initiated from a stabilizing control policy is theoretically analyzed in terms of stability of the system during the learning stage without ignoring the effects of approximation errors. This…

Bilateral trade models the task of intermediating between two strategic agents, a seller and a buyer, willing to trade a good for which they hold private valuations. We study this problem from the perspective of a broker, in a regret…

This paper investigates risk measures derived from the expected maximum deficit in a continuous-time framework and develops optimal reserve allocation strategies across multiple lines of business. We formalize the expected maximum deficit…

Controllable Markov chains describe the dynamics of sequential decision making tasks and are the central component in optimal control and reinforcement learning. In this work, we give the general form of an optimal policy for learning…

Any firm whose business strategy has an exposure constraint that limits its potential gain naturally considers expansion, as this can increase its exposure. We model business expansion as an enlargement of the opportunity set for business…

This article examines arbitrage investment in a mispriced asset when the mispricing follows the Ornstein-Uhlenbeck process and a credit-constrained investor maximizes a generalization of the Kelly criterion. The optimal differentiable and…

We study the problem of dynamic regret minimization in online convex optimization, in which the objective is to minimize the difference between the cumulative loss of an algorithm and that of an arbitrary sequence of comparators. While the…

Consider a team of agents in the plane searching for and visiting target points that appear in a bounded environment according to a stochastic renewal process with a known absolutely continuous spatial distribution. Agents must detect…

This paper studies optimal consumption and saving decisions under uncertainty about the transition dynamics of the economic environment. We consider a general optimal savings problem in which the exogenous state governing discounting,…

We examine optimization problems in which an investor has the opportunity to trade in $d$ stocks with the goal of maximizing her worst-case cost of cumulative gains and losses. Here, worst-case refers to taking into account all possible…

Risk management in dynamic decision problems is a primary concern in many fields, including financial investment, autonomous driving, and healthcare. The mean-variance function is one of the most widely used objective functions in risk…

In this paper, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or…

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…

In this paper, we study a stochastic optimal control problem with stochastic volatility. We prove the sufficient and necessary maximum principle for the proposed problem. Then we apply the results to solve an investment, consumption and…

The relationship between demand and prices of a set of products can be modeled as a linear mapping from logarithmic price changes to logarithmic changes in demand. We consider the problem of estimating the coefficient matrix of this…

In this work, we consider the optimal portfolio selection problem under hard constraints on trading amounts, transaction costs and different rates for borrowing and lending when the risky asset returns are serially correlated. No…

I characterize optimal government policy in a sticky-price economy with different types of consumers and endogenous financial constraints in the banking and entrepreneurial sectors. The competitive equilibrium allocation is constrained…

We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can…

Finding the optimal product prices and product assortment are two fundamental problems in revenue management. Usually, a seller needs to jointly determine the prices and assortment while managing a network of resources with limited…

This paper derives an optimal control strategy for a simple stochastic dynamical system with constant drift and an additive control input. Motivated by the example of a physical system with an unexpected change in its dynamics, we take the…